QQuestionMathematics
QuestionMathematics
Which three statements below are true about an acute isosceles triangle?
A. Two side measures are the same.
B. All angle measures are less than 90°.
C. One angle is obtuse.
D. Two angle measures are the same.
E. All angle measures are different.
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the definition of an isosceles triangle
- An isosceles triangle is a triangle with two sides of equal length - This means two sides have the same measure
Step 3:: Analyze the definition of an acute triangle
- An acute triangle is a triangle where ALL angles are less than 90° - No angle can be 90° or greater
Step 4:: Examine each statement carefully
Statement A: "Two side measures are the same" - This is TRUE for an isosceles triangle by definition - In an isosceles triangle, two sides have equal length Statement B: "All angle measures are less than 90°" - This describes an acute triangle - This is TRUE for an acute triangle Statement C: "One angle is obtuse" - An obtuse angle is greater than 90° - This CANNOT be true for an acute triangle - FALSE statement Statement D: "Two angle measures are the same" - This is TRUE for an isosceles triangle - When two sides are equal, the angles opposite those sides are also equal Statement E: "All angle measures are different" - This CANNOT be true for an isosceles triangle - In an isosceles triangle, two angles must be equal - FALSE statement
Final Answer
A. Two side measures are the same B. All angle measures are less than 90° D. Two angle measures are the same
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